Suppose the inverse demand curve has the following formula: p = $7 – 0.01Q. There are two firms. The cost function for the first firm is TC = 1 Q and for the second firm TC = 2Q
a) If the two firms were to combine, what Q would they produce in each division? What is the total Q, p, and profits?
b) Calculate the same for the Cournot-Nash equilibrium if they compete. (Note: If you haven’t had calculus, calculate MR for firm 1 by the usual shortcut, and set it equal to MC to get firm 1’s reaction function. When you calculate 1’s MR as a step towards 1’s reaction function, treat any term involving firm 2’s output as part of the constant that defines the price-axis intercept. Similarly to get 2’s reaction function).
c) Calculate the same for the Stackelberg equilibrium with the low cost firm as the leader. (Note: If you haven’t had calculus, it is not obvious you can solve this. I will give you full credit if you i) properly write the profit function for the first firm, incorporating the second firm’s reaction to first firm’s choice and ii) write “no calculus” on your answer sheet.)